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3 years ago

HELP ME ASAP!!

Mathematics

1 answer:

arlik [135]3 years ago

8 0

Answer:

$\huge A (n) = 5 ({2})^{n - 1} \\$

Step-by-step explanation:

The nth term of a geometric sequence is given by

$A(n) = a _ 1( {r})^{n - 1}$

a1 is the first term

r is the common ratio

From the question we have the final answer as

$A (n) = 5 ({2})^{n - 1}$

Hope this helps you

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The waiting time for a fire department to get called to a house fire is exponentially distributed with an average wait time of 1

stepan [7]

Answer:

0.319 = 31.9% probability that the wait time will be more than an additional 16 minutes

Step-by-step explanation:

To solve this question, we need to understand the exponential distribution and conditional probability.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: It has already taken 11 minutes.

Event B: It will take 16 more minutes.

Exponentially distributed with an average wait time of 14 minutes.

This means that $m = 14, \mu = \frac{1}{14}$

Probability of the waiting time being of at least 11 minutes:

$P(A) = P(X > 11) = e^{-\frac{11}{14}} = 0.4558$

Probability of the waiting time being of at least 11 minutes, and more than an additional 16 minutes:

More than 11 + 16 = 27 minutes. So

$P(A \cap B) = P(X > 27) = e^{-\frac{27}{14}} = 0.1454$

What is the probability that the wait time will be more than an additional 16 minutes?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1454}{0.4558} = 0.319$

0.319 = 31.9% probability that the wait time will be more than an additional 16 minutes

7 0

3 years ago

I need help answering this question

DiKsa [7]

Answer:

$x = 7$

Step-by-step explanation:

Given that AB and BC are perpendicular, it follows that:

m<ABC = right angle = 90°

Thus:

$75 + (x + 8) = 90$ (angle addition postulate)

Solve for x

$75 + x + 8 = 90$

$83 + x = 90$

Subtract 83 from each side

$83 + x - 83 = 90 - 83$

$x = 7$

5 0

3 years ago

Plzz answer this I'll give 11pts

andriy [413]

Answer:

pear

23.59

Step-by-step explanation:

when you divide

7 0

3 years ago

144kg in the ratio 1:3:5

bonufazy [111]

Total ratio is 1 + 3 + 5 = 9

Share for 1 = 1/9 × 144
= 16kg
Share for 3= 3/9 × 144
= 48kg
Share for 5= 5/9 × 144
= 80kg

Proof= 80 + 48 + 16 =144

4 0

3 years ago

How to solve 2.25 to the square root

Iteru [2.4K]

First find the answer without decimals
√225= 15

2.25 has two decimal places, so therefore the square root must contain 1 decimal place.
√2.25= 1.5

Final answer: 1.5
ps -1.5 is also correct but I'm not sure if that's what your teacher wants.

8 0

3 years ago